(Preferably rare) Audio/Video recordings of famous mathematicians?
The voice of John von Neumann dedicating the NORC computer in 1954 (short excerpt and full speech).
(source: washington.edu)
The wire recording is a bit murky; here is my best-effort transcript of the short excerpt:
"Those of you present who have lived with this field, and who have lived with and suffered with computing machines of various sorts, and know what kind of regime it is to invest in one, I'm sure have appreciated the fact that it appears that this machine has been completely assembled less than two months ago, has been run on problems less than two weeks ago, and yesterday already ran for four hours without making a mistake. Those of you who have not been exposed to computing machines, and who do not have the desolate feeling which goes with living with their mistakes, will appreciate what it means that a computing machine, after about two weeks of breaking in, has really a faultless run of four hours. It is completely fantastic on an object of this size; I doubt it has ever been achieved before, and it is an enormous reassurance regarding the state of the art and regarding the complexities to which one will be able to go in the future, that this has been achieved."
Here is the BibTeX reference to a printed version (which differs slightly from the speech).
@incollection{vonNeumann:54,
Author = {J. von Neumann},
Booktitle = {John von Neumann Collected Works},
Editor = {A. H. Taub},
Publisher = {Pergamon Press},
Title = {The N.O.R.C.~and Problems in High Speed Computing},
Volume = {5},
Year = 1954,
Pages = 238--247}
Jean Dieudonné, Bourbaki secretary and author of the nine-volume "Foundations of Modern Analysis" giving an interview on french television about his book "Pour l'honneur de l'esprit humain : les mathématiques aujourd'hui":
http://www.ina.fr/art-et-culture/litterature/video/CPB87005869/les-livres-du-mois.fr.html
I just found the follow audio recordings of Grothendieck:
http://cds.cern.ch/record/912518?ln=en
Unfortunately, it does not show Grothendieck "in mathematical action", but quite the contrary: In 1972, he hosted a conference at CERN entitled "Allons nous continuer la recherche scientifique?/Will we continue scientific research?"
The link is to CERN's own audio archives.